TY - JOUR T1 - The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2022 A1 - Davide Papapicco A1 - Nicola Demo A1 - Michele Girfoglio A1 - Giovanni Stabile A1 - Gianluigi Rozza KW - Advection KW - Computational complexity KW - Deep neural network KW - Deep neural networks KW - Linear subspace KW - Multiphase simulations KW - Non linear KW - Nonlinear hyperbolic equation KW - Partial differential equations KW - Phase space methods KW - Pre-processing KW - Principal component analysis KW - reduced order modeling KW - Reduced order modelling KW - Reduced-order model KW - Shifted-POD AB -

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N−width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation. © 2022 Elsevier B.V.

VL - 392 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b20101997 ER - TY - ABST T1 - The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations Y1 - 2021 A1 - Davide Papapicco A1 - Nicola Demo A1 - Michele Girfoglio A1 - Giovanni Stabile A1 - Gianluigi Rozza ER - TY - JOUR T1 - A novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems JF - Communications in Computational Physics Y1 - 2021 A1 - Kelbij Star A1 - Giovanni Stabile A1 - Francesco Belloni A1 - Gianluigi Rozza A1 - Joris Degroote AB - A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation. The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case. PB - Global Science Press VL - 30 ER - TY - JOUR T1 - A numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation JF - International Journal for Numerical Methods in Engineering Y1 - 2021 A1 - Umberto Emil Morelli A1 - Patricia Barral A1 - Peregrina Quintela A1 - Gianluigi Rozza A1 - Giovanni Stabile PB - Wiley VL - 122 UR - https://doi.org/10.1002/nme.6713 ER - TY - CHAP T1 - Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives T2 - Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions Y1 - 2020 A1 - Saddam Hijazi A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

JF - Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions PB - Springer International Publishing CY - Cham SN - 978-3-030-48721-8 UR - https://doi.org/10.1007/978-3-030-48721-8_10 ER - TY - JOUR T1 - A novel reduced order model for vortex induced vibrations of long flexible cylinders Y1 - 2018 A1 - Giovanni Stabile A1 - Hermann G. Matthies A1 - Claudio Borri PB - Elsevier {BV} VL - 156 UR - https://doi.org/10.1016/j.oceaneng.2018.02.064 ER -